Report

IDENTIFYING PATTERNS IN SPATIAL DATA Xun Zhou University of Iowa September 5, 2014 OUTLINE • Introduction • Spatial Data and Models • Statistical models • Spatial Pattern Families • Computational Challenges WHAT IS SPATIAL DATA MINING (SDM) • Identifying interesting, non-trivia, and useful patterns from large spatial datasets • “Spatial” is general – includes spatio-temporal • Examples of spatial/spatio-temporal datasets: • • • • • • • • GPS traces Facebook / Twitter check-ins Climate observations (e.g., rainfall, temperature, etc). Remotely sensed images (e.g., NASA products) Crime reports Disease maps and records Traffic statistics and road networks Sales/market price data, supply maps WHY IS SDM IMPORTANT • Location/time information brings rich context • • • Support decision making Understanding natural phenomenon Improve the quality of knowledge • London Cholera 1854 – John Snow • Modern examples • • • • Predict land cover type with limited samples Which animals often live in the same area? Detect outbreaks of diseases/crimes Find anomalous climate events Picture Courtesy: Prof. Shashi Shekhar @ UMN WHAT IS “SPECIAL” ABOUT “SPATIAL” Traditional Data Mining Spatial Data Mining Data Types Age, salary, text… (in addition) Location, shape, time … Relationships Arithmetic, Ordering, Subset… Topological, directional, metric… Statistical models Data follows i.i.d. Data is auto-correlated & heterogeneous Output pattern Diaper + beer = frequent set Diaper + beer only frequent in blue-collar neighborhoods Computation … … Picture Source: [1] SPATIAL DATA MINING COMPONENTS • Input Data • Statistical Foundations • Output patterns • Computational Process OUTLINE • Introduction • Spatial Data and Models • Statistical models • Spatial Pattern Families • Computational Challenges SPATIAL DATA TYPES • Two data representation models Vector Data (Object Model) Raster Data (Field Model) Data representation Geometric objects Continuous field with attribute functions Examples Disease reports (point) GPS traces (lines/curves) Counties, states (polygons) Satellite images Temperature map of the U.S. Vegetation cover in Africa Picture source: [2] SPATIAL RELATIONSHIPS AND OPERATIONS • Between spatial objects: • • • • • Set-oriented: Union, Intersection, Membership… Topological: Meet, within, overlap, connected… Directional: North, East, left, above, below… Metric: Distance, area, perimeter Spatial field operations • Local, Focal, Zonal, Global Individual location (elevation > 1000 ft.) A small neighborhood (slope, gradient) Part of a region (Mountain peak) Among all the locations (The Everest) OUTLINE • Introduction • Spatial Data and Models • Statistical models • Spatial Pattern Families • Computational Challenges TWO KEY FEATURES • Spatial Autocorrelation • • • The first law of geography[*]: “Everything is related to everything, but near things are more relevant than distant things”. Spatial features are usually auto-correlated or clustered rather than randomly distributed Spatial heterogeneity • Spatial patterns are not uniform globally – they vary from place to place. [*] Tobler W., (1970) "A computer movie simulating urban growth in the Detroit region". Economic Geography, 46(2): 234-240. STATISTICAL FOUNDATIONS • Spatial statistics – a brunch of statistics Models[4] Geostatistical Lattice(Areal) Point Process Scenarios Continuous space Disjoint and complete partitions of the space (e.g., grids, areas) Distribution of points Examples Temperature in US Population of counties Locations of birds Spatial Autoregressive Regression (SAR) Markov Random Field (MRF) Ripley’s K-function Cross k-function Complete Spatial Randomness (CSR) Major Kriging (spatial techniques interpolation) * These are statistical models (like normal distribution) and may not lineup with data representation models. SPATIAL NEIGHBORHOOD • A collection of nearby location/spatial object • • Adjacent/connected objects/locations Within a certain distance r • The W-matrix: A B C D 0 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 0 0.5 0.5 0 0.5 0 0 0.5 0.5 0 0 0.5 0 0.5 0.5 0 OUTLINE • Introduction • Spatial Data and Models • Statistical models • Spatial Pattern Families • Computational Challenges SPATIAL PATTERN FAMILIES • A comparison with traditional DM tasks Traditional Data Mining Pattern Families Spatial Data Mining Pattern Families Prediction/Classification Spatial Prediction/Geographic Classification Clustering Spatial Clustering/Hotspot detection Anomaly Detection Spatial Anomaly/Outlier Detection Association Rule Mining Spatial Co-location Patterns SPATIAL PREDICTION • C4.5 results on land cover data [5] Traditional classifiers based on i.i.d. and global model • • Linear regression, Decision Tree, SVM, CART, etc. Spatial auto-correlation and variation are not modeled • Predicting land cover types, location-based recommendation • Regression • Linear regression SAR GWR = + = + + = ′ + ′ ( ′ ′ ) Spatial Decision Tree[5] • • Information gain function: add spatial autocorrelation measure Spatial Decision rules: Traditional Illustration of focal-test-based f(x) > 1? Left : Right Flip if neighbors classified differently spatial decision tree[5] SPATIAL OUTLIER DETECTION • Traditional Anomaly Detection • • Data is anomalous w.r.t. global data distribution Spatial outlier[6] Data is anomalous w.r.t. its neighbors (discontinuity) • Finding Suspicious buildings, broken sensors, or other points of interest… • Methods: • Variogram clouds • Moran scatterplot • Spatial Statistic (S) • 1 1 1 2 4 5 1 5 1 2 4 5 1 1 1 2 4 5 2 2 2 2 4 5 4 4 4 4 4 5 5 5 5 5 5 5 1-D spatial data and distribution [1] SPATIAL ASSOCIATION • Spatial Co-location pattern[7] • • • Given a number of spatial object types and instances Find sets of types that are frequently located in proximity Example: {Fox, Rabbits}, {Nile Crocodiles, Egyptian Plover} Frequent item set Co-location Comment Transactions Neighbor set Space is continuous, no transactions Support, Confidence Participation index PI = min(AB/A, AB/B) {‘+’, ‘x’}, {‘o’, ‘*’} Pictures source: [1] SPATIAL CLUSTERING • Grouping spatial objects into clusters such that • • Intra-cluster similarity is maximized Inter-cluster similarity is minimized • Detecting communities, crowds, building blocks, etc. • Is there a clustering tendency of data in space (point data)? 1. Hierarchical 2. Partitioning: k-means 3. Density-based: DBSCAN Picture Courtesy: Prof. Shashi Shekhar @ UMN Complete Spatial Randomness(CSR) Clustered Di-clustered SPATIAL HOTSPOT DETECTION • Special case of clustering Identify regions with high density - not a complete partitioning of data • Ignore noise or sparse clusters • Crime/disease outbreaks, traffic jam, water pollution… • Statistical significance – avoid random clusters • • Density-based approaches: DBSCAN[8] DBSCAN output on clustered dataset: min neighbors=3, radius=7 100 DBSCAN output on CSR dataset: min neighbors=3, radius=7 100 • Statistical tests – spatial scan statistics[9] (public health) 90 90 80 Spatial Scan Statistics 70 70 60 60 50 50 Y Y 80 40 40 30 30 20 20 10 0 DBSCAN Spatial Scan Statistics 10 0 DBSCAN NEW DIMENSIONS OF SPATIAL PATTERNS • Patterns on Spatial Networks Hotspots (Dangerous routes with high risk of accidents)[10] • Clusters (Crimes along the streets, bus/bike route planning) • Predictions • • Irregular/complex-shaped Spatial Patterns • Complex-shaped clusters (terrain constraints) • Irregular Hotspots (gerrymander …) Results on pedestrian fatality data from Orlando, FL.[10] ADDING TIME • Input data • Spatial data Spatio-temporal data Time series • Vector: point sequences, polygon series… • Raster: image sequences, spatial time series (a time series at each grid) • • • Relationship: before, after, during, simultaneous, … Statistical Foundations • • Markov Chain, Hidden Markov Model… Spatiotemporal Statistics ADDING TIME - PATTERNS Spatial Data Mining Pattern Families Spatiotemporal Patterns Spatial Prediction/Geographic Classification ST prediction (trajectory prediction, climate projection, market prediction…) Spatial Anomaly/Outlier Detection ST Anomaly (abnormal climate events, traffic sensors…) Spatial Co-location Patterns Co-occurrence[11], Cascading pattern[12] (Crime associations, potential social connections) Spatial Clustering/Hotspot detection Space-time clusters[13] (disease monitoring) Moving clusters (flocks, fleet, etc) Emerging Hotspot (New market…) Spreading hotspot (Strikes, Arabic Spring…) ADDING TIME – NEW PATTERNS • New Dimensions of Temporal Information • • Change Repeating/periodicity Temporal dimensions Spatiotemporal Patterns Change Change Footprint Pattern Discovery[2] - Where and When changes occur - Climate change, Business grow, urban sprawl, etc Change Prediction - Where and When will change occur Repeating/periodic Finding periodic travel patterns, schedules, habits 0.4 NDVI 0.35 2001 2006 2012 0.3 An annual increase of 11.5%, 2001-2012 0.25 0.2 2000 2002 Vegetation increase in Saudi Arabia due to irrigation [14] 2004 2006 Year 2008 2010 2012 CHANGE FOOTPRINT PATTERNS Static Local Time Between snapshots Time Focal Point in time series Time Zonal Interval in time series Time OUTLINE • Introduction • Spatial Data and Models • Statistical models • Spatial Pattern Families • Computational Challenges COMPUTATIONAL CHALLENGES Neighborhood graph generation • Parameter Estimation • Better Interpretability • Complex-shapes of pattern • • Filter-n-refine approach Pattern Completeness High combinatorics of patterns • Enumeration and pruning strategies • • Interest measure property • • • Conceptual Modeling balance Interest measure DP or Greedy may not be used HPC with Spatial Data Mining • Pattern Interpretability • Parallel/Cloud Computing GIS on Hadoop (ESRI) Algorithm Design Computational Scalability SUMMARY • What is SDM and why it’s important • What’s special about spatial • Pattern families, potential directions and applications • Computational Challenges ACKNOWLEDGEMENT • This presentation is prepared based on materials from Prof. Shashi Shekhar and the Spatial Database and Spatial Data Mining Group at the University of Minnesota (http://www.spatial.cs.umn.edu/). REFERENCES AND READINGS [1]. Shekhar, Shashi, et al. "Identifying patterns in spatial information: A survey of methods." Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery 1.3 (2011): 193-214. [2]. Xun Zhou, Shashi Shekhar, and Reem Y. Ali. "Spatiotemporal change footprint pattern discovery: an inter‐disciplinary survey." Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery 4.1 (2014): 1-23. [3]. Shashi Shekhar and Sanjay Chawla. Spatial Database: A Tour. Prentice Hall 2003. [4]. Banerjee, Sudipto, Alan E. Gelfand, and Bradley P. Carlin. Hierarchical modeling and analysis for spatial data. CRC Press, 2004. [5]. Jiang, Z., Shekhar, S., Zhou, X., Knight, J., & Corcoran, J. (2013, December). Focal-test-based spatial decision tree learning: A summary of results. In Data Mining (ICDM), 2013 IEEE 13th International Conference on (pp. 320-329). IEEE. [6]. Shekhar, Shashi, Chang-Tien Lu, and Pusheng Zhang. "A unified approach to detecting spatial outliers." GeoInformatica 7, no. 2 (2003): 139-166. [7]. Y Huang, S Shekhar, H Xiong, Discovering colocation patterns from spatial data sets: a general approach. Knowledge and Data Engineering, IEEE Transactions on 16 (12), 1472-1485 [8]. Ester, Martin; Kriegel, Hans-Peter; Sander, Jörg; Xu, Xiaowei (1996). "A density-based algorithm for discovering clusters in large spatial databases with noise". In Simoudis, Evangelos; Han, Jiawei; Fayyad, Usama M. Proceedings of the Second International Conference on Knowledge Discovery and Data Mining (KDD-96) [9]. Kulldorff, Martin. "A spatial scan statistic." Communications in Statistics-Theory and methods 26.6 (1997): 1481-1496. [10]. Dev Oliver, Shashi Shekhar, Xun Zhou, Emre Eftelioglu, Michael Evans, Qiaodi Zhuang, James Kang, Renee Laubscher and Christopher Farah. Significant Route Discovery: A Summary of Results. In GIScience 2014 (to appear). [11]. Celik, Mete, et al. "Mixed-drove spatiotemporal co-occurrence pattern mining." Knowledge and Data Engineering, IEEE Transactions on 20.10 (2008): 1322-1335. [12]. Mohan, Pradeep, Shashi Shekhar, James A. Shine, and James P. Rogers. "Cascading spatio-temporal pattern discovery." Knowledge and Data Engineering, IEEE Transactions on 24, no. 11 (2012): 1977-1992. [13]. Daniel B. Neill, Andrew W. Moore, Maheshkumar Sabhnani, and Kenny Daniel. Detection of emerging space-time clusters. Proceedings of the 11th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, 218-227, 2005 [14]. Xun Zhou, Shashi Shekhar, Dev Oliver. "Discovering Persistent Change Windows in Spatiotemporal Datasets: A Summary of Results". In 2nd ACM SIGSPATIAL International Workshop on Analytics for Big Geospatial Data (BigSpatial-2013), Nov 5, 2013, Orlando, Florida, USA.